Quantum simulations of a freely rotating ring of ultracold and identical bosonic ions

Robicheaux, F.; Niffenegger, K.

doi:10.1103/physreva.91.063618

Cited by 6 publications

(5 citation statements)

References 19 publications

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“…Such a phenomenon could be in principle realized in ultra-cold atoms laboratory. The idea of time crystals initiated a novel field of research and inspired many physicists (Chernodub, 2013;Faizal et al, 2016;Mendonca and Dodonov, 2014;Robicheaux and Niffenegger, 2015;Yamamoto, 2015).…”

Section: B Origin Of Time Crystals: Spontaneous Breaking Of Continuou...mentioning

confidence: 99%

Time crystals: a review

2017

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Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals-the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek's idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.

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Section: B Origin Of Time Crystals: Spontaneous Breaking Of Continuou...mentioning

confidence: 99%

Time crystals: a review

2017

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“…(5). In the following we assume α = 0 and that the initial state |ψ 0 corresponds to the lowest energy eigenstate in the subspace with the total momentum P N and investigate if measurement of particles positions breaks the continuous time translation symmetry and pushes the system to periodic motion that can live infinitely long in the limit of N → ∞ [4,9,13,17]. Eigenstates of the Hamiltonian (1) with α = 0 can be found with the help of the Bethe ansatz [31].…”

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confidence: 99%

“…However, at the same time the original proposition has been put in question [5,6]. While the discussion interestingly evolved [7][8][9][10][11][12][13] strong arguments have been presented [14][15][16] against the existence of time crystals. The proposals, nevertheless, became inspiring and triggered a new field of research.…”

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confidence: 99%

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Time Crystal Behavior of Excited Eigenstates

2017

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In analogy to spontaneous breaking of continuous space translation symmetry in the process of space crystal formation, it was proposed that spontaneous breaking of continuous time translation symmetry could lead to time crystal formation. In other words, a time-independent system prepared in the energy ground state is expected to reveal periodic motion under infinitely weak perturbation. In the case of the system proposed originally by Frank Wilczek, spontaneous breaking of time translation symmetry can not be observed if one starts with the ground state. We point out that the symmetry breaking can take place if the system is prepared in an excited eigenstate. The latter can be realized experimentally in ultra-cold atomic gases. We simulate the process of the spontaneous symmetry breaking due to measurements of particle positions and analyze the lifetime of the resulting symmetry broken state. 03.75.Lm, Hamiltonians of condensed matter systems are invariant under translation of all particles by the same vector in space and so are the eigenstates. Consequently probability density for detection of a single particle must be uniform in space if a system is prepared in the ground state or any other eigenstate. Space crystals emerge due to spontaneous symmetry breaking that can be induced by an external perturbation or by, e.g., measurements of particle positions. If the single particle probability density is uniform but the density-density correlation function reveals periodic behavior, measurement of a position of a particle breaks the continuous space translation symmetry and the probability density for the detection of a next particle shows crystalline structure [1, 2]. In the thermodynamic limit, the lifetime of the symmetry broken state goes to infinity and the stable space crystal is formed.Similar phenomenon was postulated to exist in the time domain [3]. A spontaneous breaking of the continuous time translation symmetry in the ground state of the model system was suggested to lead to a periodic motion of a nonuniform density. Soon the other experiment involving trapped ions in a ring [4] was proposed. However, at the same time the original proposition has been put in question [5,6]. While the discussion interestingly evolved [7][8][9][10][11][12][13] strong arguments have been presented [14][15][16] against the existence of time crystals. The proposals, nevertheless, became inspiring and triggered a new field of research. It turns out that, by analogy to condensed matter physics, where space periodic potentials allow for modeling of space crystals, periodically driven systems can model crystalline behavior in time [17]. Anderson localization and Mott insulator phase in the time domain can be realized [18][19][20] and spontaneous breaking of discrete time translation symmetry to another discrete symmetry can be investigated [17]. The latter phenomenon, termed discrete time crystal, was recently observed in two experiments [21,22] following independent theoretical suggestions [23][24][25][26][27][28][29]. Thos...

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“…Hence, we focus only on the dynamics of the rotation and assume that all other modes are cooled to the standard Doppler limit without further complications. However, we note that for the experiments relating to the symmetrization of the ion wavefunction it will necessary to cool all modes of the ion string to the motional ground state to guarantee indistinguishability of the ions [28].…”

Section: Laser Coolingmentioning

confidence: 99%

Surface traps for freely rotating ion ring crystals

Wang

Noel

et al. 2015

J. Phys. B: At. Mol. Opt. Phys.

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We present a design of an r.f. trap using planar electrodes with the goal to trap on the order of 100 ions in a small ring structure of diameters ranging between 100 µm and 200 µm. In order to minimize the influence of trap electrode imperfections due to the fabrication, we aim at trapping the ions around 400 µm above the trap electrodes. In view of experiments to create freely rotating crystals near the ground state, we numerically study factors breaking the rotational symmetry such as external stray electric fields, local charging of the trap electrodes, and fabrication imperfections. We conclude that these imperfections can be controlled sufficiently well under state-of-the-art experimental conditions to allow for freely rotating ion rings even at energies comparable to the ground state energy of the rotational degree-of-freedom.

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Quantum simulations of a freely rotating ring of ultracold and identical bosonic ions

Cited by 6 publications

References 19 publications

Time crystals: a review

Time crystals: a review

Time Crystal Behavior of Excited Eigenstates

Surface traps for freely rotating ion ring crystals

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